1. Field of the Invention
This invention relates to the shape of gear teeth. Specifically it relates to gearing having characteristics that eliminate transmission error at all loads, so that the dynamic increment of load is also eliminated at all loads. This eliminates the main harmonics of gear noise and also greatly increases torque capacity. The invention discloses how these desirable performance characteristics can be achieved by a means of an improved type of tooth modification manufacturable by methods that make the gears less expensive than conventional gears.
2. Prior Art
The invention comprises additions to and improvements on the concepts disclosed in U.S. Pat. No. 5,083,474 (hereinafter Reference 1) and my copending U.S. Pat. application Ser. No. 08/043,375 now U.S. Pat. No. 5,341,699 (hereinafter Reference 2) for which the issue fee has been paid. Reference 2 is not prior art, and I hereby incorporate by reference the entire content thereof into this application. The special performance advantage of the gearing disclosed in Reference 1, which is called "Zero Transmission Error" (ZTE) gearing, is greatly reduced noise. The special performance advantage of the gearing disclosed in Reference 2, which is called "Zero Dynamic Increment" (ZDI) gearing, is substantially improved torque capacity. Both these performance advantages, however, were achieved by a means that had two disadvantages: The first disadvantage in the disclosures of the cited References resides in the proposed crown forms. FIG. 10 in Reference 1 and FIG. 6 in Reference 2 disclose crown forms that are smooth continuous curves starting at the midline of the face width. The general mathematical form of these curves is that of a continuous exponential curve of the Ax.sup.n variety. There are three difficulties with such a crown form: (1) It has only two parameters, A and n, so that crown forms based on it can have only two precision points at which the static transmission error is zero; (2) the two parameters are locked together in a single expression, so that neither parameter can be iterated independently; and (3), the basic parabolic shape of the crown curves tends to produce a nonlinear load-deflection curve, whereas the need is for a load-deflection curve that is close to linear, because only one of the six sources of gear tooth deflection, the Hertz deflection, is nonlinear.
The second disadvantage in the disclosures of References 1 and 2 is that the special tooth surface modification pattern proposed, which was called "differential crowning," was a special form of what is generally called "topological modification." Unfortunately, there is only one grinder that has the capabilities to form topological modifications, either directly or by fabrication of specially designed shaving cutters. The company that made this special grinder has stopped production of it. Only about 30 or 40 of these grinders exist in the entire world, and nearly all of them are owned by companies that use them in-house for sharpening conventional shaving cutters. Because this special topological grinder is in such short supply and forms modifications in a slow, point-by-point manner, manufacturing costs for making the new gearing boded to be greater than that of conventional gearing.
In addition to the above-mentioned References 1 and 2, U.S. Pat. No. 3,982,444 (hereinafter Reference 3), may also be considered to be relevant prior art.